The problem with checking gifts (wrapped or not) is that they are new, and things like clothing still have identifying tags on them. Thieves find such items VERY attractive, because they can take those brand-new items back to the store and and claim that they received them as a gift. Then they get store credit for the items, pick out new things, and or even then take THOSE things to another branch of the same store for a cash refund.
If you feel that you have to put new items in checked baggage, take the precaution of taking the items out of their original store packaging, and removing ALL tags that mark where they came from.
The luggage theft problem is worse now than it used to be, not because baggage-handlers are so much more honest than TSA agents, but because representatives of two different corporate bodies now have access to your bags, creating a double-blind for the thieves to hide behind. The airlines can blame it on TSA, while TSA can blame it on the airlines, and thus neither side watches their own people as closely as they should.